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mario wrote two unit fractions on his paper. (a unit fraction has one as its numerator.) the denominators of the fractions are consecutive integers. if the sum of the fractions is 7/24, what are the two unit fractions?

Sagot :

We let X be the first integer and X + 1 be the second integer. We write: (1/X) + [1/(X + 1)] = 7/24 --> Multiply (X)(X + 1)(24) to the whole equation to leiminate the denominators: [24X(X + 1)] {(1/X) + [1/(X + 1)] = 7/24} --> [24(X + 1)] + 24X = 7(X)(X + 1) --> 24X + 24 + 24X = 7X^2 + 7X --> 0 = 7X^2 - 41X - 24 --> X = 6.39, -0.536. 1/6.39 and 1/7.39